Request a User’s Email Address
Requesting a user’s email address requires your application to be whitelisted by Twitter. To request access, please use this form.

Once whitelisted, the “Request email addresses from users” checkbox will be available under your app permissions on apps.twitter.com. Privacy Policy URL and Terms of Service URL fields will also be available under settings which are required for email access. If enabled, users will be informed via the oauth/authorize dialog that your app can access their email address.